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Toward Tractable Global Solutions to Maximum-Likelihood Estimation Problems via Sparse Sum-of-Squares Relaxations
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.ORCID iD: 0000-0001-7823-2993
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH Royal Institute of Technology. (System Identification)ORCID iD: 0000-0001-5474-7060
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. (System Identification)ORCID iD: 0000-0002-9368-3079
2019 (English)Conference paper, Published paper (Refereed)
Abstract [en]

In system identification, the maximum-likelihood method is typically used for parameter estimation owing to a number of optimal statistical properties. However, in many cases, the likelihood function is nonconvex. The solutions are usually obtained by local numerical optimization algorithms that require good initialization and cannot guarantee global optimality. This paper proposes a computationally tractable method that computes the maximum-likelihood parameter estimates with posterior certification of global optimality via the concept of sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method can be applied to certain classes of discrete-time linear models. This is achieved by taking advantage of the rational structure of these models and the sparsity in the maximum-likelihood parameter estimation problem. The method is illustrated on a simulation model of a resonant mechanical system where standard methods struggle.

Place, publisher, year, edition, pages
2019.
Keywords [en]
Maximum likelihood, LMI, non-convex, relaxation, sum-of-squares, sparse
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-255811OAI: oai:DiVA.org:kth-255811DiVA, id: diva2:1342060
Conference
58th IEEE Conference on Decision and Control (CDC 2019)
Funder
Vinnova, 2016-05181
Note

QC 20190813

Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-13Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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